Evaluation of the molecular static and dynamic first hyperpolarizabilities

de Wergifosse, Marc [UCL] Liégeois, Vincent [Laboratoire de Chimie Theorique, Unite de Chimie Physique Theorique et Structurale, Universite de Namur, Rue de Bruxelles, 61, B-5000 Namur, Belgium] Champagne, Benoît [Laboratoire de Chimie Theorique, Unite de Chimie Physique Theorique et Structurale, Universite de Namur, Rue de Bruxelles, 61, B-5000 Namur, Belgium]

By considering two prototypical p-conjugated compounds, several technical aspects associated with the evaluation of the first hyperpolarizabilities have been addressed in this article, that is, (i) the automatization of the Romberg’s scheme to improve the numerical accuracy in the finite field method, (ii) the evaluation of the frequency dispersion at correlated levels using approximate schemes, and (iii) the deviations from Kleinman’s symmetry conditions. It results from this study that accurate numerical derivatives can be obtained by resorting to the Romberg’s method and by analyzing the Romberg’s table in terms of two quantities, the field error and the iteration error. Indeed, the resulting first hyperpolarizability values are in close agreement with those obtained using an analytical differentiation procedure. The reliability of the multiplicative and additive approximate schemes to describe the frequency dispersion at correlated levels from using HF (Hartree-Fock) frequency dispersion has been confirmed to be limited to large wavelengths or far-from-resonance wavelength regions. Kleinman’s symmetry conditions have been assessed, showing that for off-diagonal components of these two p-conjugated compounds, the deviations could be substantial. Nevertheless, good accuracy can be achieved for experimentally related quantities like bHRS because the diagonal tensor components are dominant.